Determine the required size for a rectangular floor beam made of timber and check the beam deflection under live load using both ASD $(20$ pts$)$ and LRFD $(20$ pts$)$ methods.

Assume the following:

Live load $=75l\frac{b}{f}{t}^2$

Dead load $=15l\frac{b}{f}{t}^2$

Allowable stress in bending $=F_b=1400l\frac{b}{i}{n}^2$

Allowable shear stress $=F_v=170l\frac{b}{i}{n}^2$

Allowable bearing stress $=F_{bg}=600l\frac{b}{i}{n}^2$

Assume a bearing area of $2\mathrm{.}5$ in$.*2$ in$.$

Allowable deflection $==\frac{L}{360}$ for live loads and $\frac{L}{240}$ for live plus dead loads.

Assume also that $E=1\mathrm{.}6*106l\frac{b}{i}{n}^2,L=18\mathrm{.}0ft,$ and $a=18in.$

Format conversion factor for bending stress $K_F$:$2\mathrm{.}54($LRFD only$)$

Resistance Factor for bending stress $$:$0\mathrm{.}85($LRFD only$)$

Time Effect Factor bending stress $$ : $0\mathrm{.}6($LRFD only$)$

Format conversion factor for shearing stress $K_F$:$2\mathrm{.}88($LRFD only$)$

Resistance Factor for shearing stress $$:$0\mathrm{.}75($LRFD only$)$

Time Effect Factor shearing stress $$ : $0\mathrm{.}6($LRFD only$)$

Format conversion factor for bearing stress $K_F$:$2\mathrm{.}08($LRFD only$)$

Resistance Factor for bearing stress $$:$0\mathrm{.}9($LRFD only$)$

Time Effect Factor bearing stress $$ : $0\mathrm{.}6($LRFD only$)$